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Throughput-distortion computation of generic matrix multiplication: Toward a computation channel for digital signal processing systems

Anastasia, D; Andreopoulos, Y; (2012) Throughput-distortion computation of generic matrix multiplication: Toward a computation channel for digital signal processing systems. IEEE Transactions on Signal Processing , 60 (4) 2024 -2037. 10.1109/TSP.2011.2176337. Green open access

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Abstract

The generic matrix multiply (GEMM) function is the core element of high-performance linear algebra libraries used in many computationally demanding digital signal processing (DSP) systems. We propose an acceleration technique for GEMM based on dynamically adjusting the imprecision (distortion) of computation. Our technique employs adaptive scalar companding and rounding to input matrix blocks followed by two forms of packing in floating-point that allow for concurrent calculation of multiple results. Since the adaptive companding process controls the increase of concurrency (via packing), the increase in processing throughput (and the corresponding increase in distortion) depends on the input data statistics. To demonstrate this, we derive the optimal throughput-distortion control framework for GEMM for the broad class of zero-mean, independent identically distributed, input sources. Our approach converts matrix multiplication in programmable processors into a computation channel: when increasing the processing throughput, the output noise (error) increases due to: (i) coarser quantization; and (ii) computational errors caused by exceeding the machine-precision limitations. We show that, under certain distortion in the GEMM computation, the proposed framework can significantly surpass 100% of the peak performance of a given processor. The practical benefits of our proposal are shown in a face recognition system and a multilayer perceptron system trained for metadata learning from a large music feature database.

Type:Article
Title:Throughput-distortion computation of generic matrix multiplication: Toward a computation channel for digital signal processing systems
Open access status:An open access version is available from UCL Discovery
DOI:10.1109/TSP.2011.2176337
Publisher version:http://dx.doi.org/10.1109/TSP.2011.2176337
Language:English
Additional information:© 2012 IEEE. Personal use of this material (accepted version) is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Electronic and Electrical Engineering

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